D1 chapter 2 - Graphs and Networks

In this chapter you will learn

• how graphs and networks can be used to make mathematical models
• definitions of key terms in graphs and networks
• about some special types of graph
• how to represent graphs and networks with matrices

D1 section 2.1

How graphs and networks can be used to create mathematical models.
definitions:

• a graph consists of points (called vertices or nodes) which are connected by lines (edges or arcs).
• if a graph has a number associated with each edge (usually called its weight) then the graph is known as a weighted graph or network.

D1 section 2.2

Basic terminology of graph theory:
In this graph, G:

• the vertices (or nodes) are: A, B, C, D, E and F
• {A, B, C, D, E, F} is the vertex set.
• the edges (or arcs) are AB, AC, AF, BC, BD, CE and DE
• {AB, AC, AF, BC, BD, CE, DE} is the edge set.

D1 Exercise 2A

• D1 Exercise 2A worked solutions:

• Questions similar to this exercise: